You didn’t answer my question at all though. If we want to represent an FR from 20-20khz, what time window would be appropriate for the impulse response? Or have you actually not done this math before?

Perfect. What ~time gate would that signal have sufficiently decayed? (per your DTFT link)

Have you done that with a 20-20k FR and looked at the time domain?

I’m getting bombarded with a lot of “nuh uh”s, your comment included, despite my mathematical explanation above. Would you care to mathematically demonstrate your claim that they are linked?

Not a fan of the snide remark. Would you care to at least substantiate this “basic principle” with a link, or did you just intend to negate my position via name calling?

Sure, but like you said, it’s a phase shift in the frequency domain. It doesn’t alter the magnitude of the FR spectrum, just the imaginary vs real distribution. For the purposes of measuring audio equipment, we can pretty safely ignore that distinction you raise, and it doesn’t negate my point that time and frequency domain are not equivalent in the OP.

I don’t understand your comment that there is no need to get into the math. Do you realize the original comment was misunderstanding the exact math I was talking about?

To make sure you’ve read my post… I’m not saying the math tells us anything. I replied to a comment that claims that impulse response is exactly the same as frequency response, and therefore we could safely ignore impulse response graphs. The math says that isn’t true. Therefore I claim we need controlled studies to understand what an impulse response can or cannot tell us before anyone knows what to interpret from them.

This is an online audio fallacy / myth. Time domain and frequency domain are only equivalent if both are infinite.

I wrote out a longer response in replay to a different comment, but an easy way to see the issue with what you’re starting is to ask how bass response would appear on the above chart (which is completely flat past ~0.002 seconds. One cycle at 200 hz is 0.005 seconds. One cycle at 20 hz is 0.05 seconds! How could you possibly infer anything about the bass response of that unit from that graph? How then can you say that graph is telling us only and exactly what the FR is?

If we want to get real technical, you’d also have to address how certain time domain translations do NOT alter the frequency domain (see shift property of the Fourier transform). That is, time delays do not alter the frequency domain. Relative timing information is very likely lost due to these two effects (representing the freq domain on a finite spectrum and not accounting for time delays).

Please stop propagating this misunderstanding that time and frequency are 100% equivalent

Two quick fallacies to call out here A) the one everyone misses: time domain = frequency domain if you have infinite time and infinite frequencies. But if I showed you a frequency response of a song on only 1-40,000hz (or whatever, limits exaggerated to make the point), there would be infinite different songs that have that exact same FR. Simplest way to understand this is imagine if I played a song in reverse. It’d have the same FR from 1-40khz. Imagine I took the first second of a song and moved it to the end of that song. Also same FR. You could absolutely take the Fourier transform of a song and convert it to frequency domain. But you’d need to go into the microhertz to fully represent it in FR. People like to cite the frequency & time domain equivalencies to say that the time domain doesn’t matter at all just because you have an FR graph that goes from 20hz-20khz. This concept gets misquoted and abused in lots of arguments about interpreting FR plots. It doesn’t conclude what people want it to, and if people want to claim time domain plots are 100% irrelevant, the onus is still on them to demonstrate this with controlled studies. We can do some fancier math to put some constraints around my argument, but the original point needs to be made that time and frequency domains are only equivalent if both are infinite. Source: I am a mathematician who studied signal processing

B) Nobody said anything about subjective listening or hearing impulse response. I know you cite it as your own experience, but that feels a bit like a straw man argument. Original post made a conclusive assertion that impulse response is irrelevant

Has this claim actually been tested? This sounds a lot like conjecture

You’re in the endgame now…

Don’t worry. Just enjoy!